The generator matrix

 1  0  0  0  1  1  1  X  1  1  X  1  1  1
 0  1  0  0  X  1  1  1 X+1 X^2+X+1  0 X^2+X X^2  0
 0  0  1  0 X+1  1  X X+1  1  0  1  0  X  0
 0  0  0  1  1 X^2+X X+1  1  1  X  1 X+1 X+1  0
 0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+52x^8+228x^9+723x^10+1760x^11+4001x^12+6172x^13+6847x^14+6272x^15+3966x^16+1724x^17+745x^18+224x^19+43x^20+4x^21+5x^22+1x^24

The gray image is a linear code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 1.93 seconds.